The Transverse Geometry of Tiling Spaces
Jean Bellissard (Georgia Tech and University of Muenster)
Tuesday 29th November, 2016 16:00-17:00 Maths 522
Given a tiling the tiling space will be constructed using examples. It can be represented as the boundary of a tree graph with a root. The Geometry will be represented through a spectral triple. The definition will be provided with examples. The Pearson-Palmer Spectral triple for the Tiling Space will be described. The Haussdorff dimension and the Hausdorff measure of the tiling space are computable from the PP spectral triple. At last the Pearson Laplacian acting on the tiling space will be described and together with its diffusion properties.